Certain Orthodox and Eastern Catholic Patriarchs are successors of Peter directly, as the Pope of Rome is, since Peter personally ordained his successor in Antioch and ordained Mark and sent him to Alexandria.
Eastern Orthodox, Byzantine Catholics and some Oriental Orthodox view all bishops as successors of Peter in the sense of holding the fullness of the episcopacy. There are only three orders that include deacon, priest and bishop, not a 4th called Patriarch/Pope - the Pope is in their view the same as any other bishop, with a primary role of honor.
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